Quant Boosters - Hemant Malhotra - Set 6


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    (a + b)^2 - (a^2 + b^2) = 2 * (ab)
    (a + b + c)^2 - (a^2 + b^2 + c^2) = 2 * (ab + bc + ca)
    and so on
    (1 + 2 + 3.........12)^2 - (1^2 + 2^2......12^2) = 2 * (required answer)
    so required value=5434/2=2717


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q26) There are three runners viz , Nishant , Deepak and Mohit who jog on the same path. Nishant goes jogging every two days. Deepak goes jogging every four days. Mohit goes jogging every seven days. If its the first day that they started this routine, what is the total number of days that each person will jog by himself in the next seven weeks?
    (a) 12
    (b) 13
    (c) 14
    (d) 15
    (e) 16


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Nishant = 25 days,
    Deepak = 13 days,
    Mohit = 7 days.
    Nishant jogs on days 1,3,5,7,.....49, and Deepak jobs on days 1,5,9,.....49, and Mohit jogs on days 1, 8, 15, 22,...43.
    when Deepak jogs, Nishant will always be jogging also, so Deepak jogs 0 days alone.
    Nishant jogs 25-13=12 days without Deepak also jogging,
    but Mohit jogs on 4 odd numbered days, 2 of which Deepak also jogs, giving us 12-4+2=10 days that Nishant jogs alone.
    Nishant jogs on every odd numbered day, so Mohit jogs alone only on even numbered days.
    Because there are 4 odd numbered days , there are 3 even numbered days, so Mohit jogs alone on 3 days.
    so
    Nishant: 10
    Deepak: 0
    Mohit: 3
    so 10+0+3=13


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q27) The sum of all the possible values of integral a such that (a^2-2a)^(a^2+47) = (a^2-2a)^(16a-16) is
    (a) 16
    (b) 17
    (c) 18
    (d) 19
    (e) none


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    a^2 - 2a will be equal to 0 or 1 or -1 then it’s possible
    when a^2 - 2a = 0
    so a=0,2
    when a^2-2a=1 then not real values
    a^2-2a=-1 so a=1
    so 0,1,2 these three possible values
    now when same base
    ((a^2+47)= (16a-16))
    so a^2-16a+63=0
    so a=7,9
    so sum 0+1+2+7+9=19


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q28) Ten liters content of a milk water solution, which contain milk and water in the ratio 7:3 are removed and replaced with water to bring down the concentration of milk by 10% points. The amount (in liters) of water that needs to be added to the resulting solution in order to reduce the concentration of milk to 50% is?


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    When water= 7 liter extra
    milk =7 liter decrease
    then decrement of milk =10%
    x * 10/100=7 so x=70 so total solution=70
    now initially there was 49 liter milk and 21 liter water
    but 7 liter milk reduced so 42 milk and 21+7=28 liter water
    so (28+a)=(70+a) * 50% so a=14
    If a and b are two real numbers such that a + b = 1, then find the maximum possible value of the product of (a^a x b^b) and (a^b and b^a)
    a^(a+b) * b^(a+b)
    a * b
    if a+b=1 and we want max a * b so 1/4


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q29) Let {Vn} be a sequence such that V1 = 2, V2 = 1 and 2 Vn – 3 Vn-1 + Vn–2 = 0 for n > 2, then find the value of V9.


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    V1=2
    V2=1
    2Vn-3Vn-1+Vn-2=0 for n > 2
    now put n=3
    so 2V3-3V2+V1=0
    so 2V3=3V2-V1
    so 2V3=3-2=1 so V3=1/2
    now put n=4
    2V4-3V3+V2=0
    2V4=3 * 1/2 -1=1/2 so V4=1/4
    now check V1=2,V2=1,V3=1/2,V4=1/4 and So on so this is GP


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q30) sherlock homes and dr. watson have to travel from rajiv gandhi chowk to indira gandhi international airpot via the metro. they have enough coins of 1,5,10,25 paise. sherlock homes agrees to pay for dr. watson, only if he tells all the possible combination of coins that can be used to pay for the ticket. How many combinations are possible, if the fare is 50 paise?
    a) 52
    b) 49
    c) 45
    d) 44


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    a + 5b + 10c + 25d = 50 ,
    Put d = 0, a + 5b + 10c = 50 now solve this
    Put d = 1 then d = 2


 

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